Nonlubricated formed gearing



6, 1965 w. s. RO'UVEROL. 33692408 NONLUBRICATED FORMED' GEARING BINVENTOR.

W/LZ/AM ROUVEROL BY M 4T TORNEY Feb. 16, 1965 w. s. ROUVEROLNONLUBRICATED FORMED GEARING 3 Sheets-Sheet 2 Filed Feb. 7, 1963INVENTOR. WILL/AM 5. ROUVEROL A T TOEWEV Feb. 16, 1965 w. s. RO'UVEROILmuwsmcmso JEQRMED LGEARING L3 E-Sheets-Sheet 3 Filed Feb. 7, 1963INVENTOR. WILL/14M 5. ROUVEROL M mob-4 ATTORNEY United States Patent Ofiice greases Patented Feb. 16, 1955 3,l6,498 N GNLUBRECATEB F'Gi lbll)GEA'RENG William S. Rous'eroi, lilld Shattucl: Ave, Bcrlreley, Calii.Filed Feb. 7, 1963, Ser. No. 255,$2 4 Claims. or. "rsim zation costs perset of gears; second, conventional gear ing has high-pressure line orpoint sliding contact between mating teeth, so that lubrication must beprovided to pre vent wear, and this in turn adds the expense of ahousing and oil seals to the high initial cost of the gearing itself.

The present invention discloses constructions which avoid both of theselimitations and thereby opens the field of heavy duty power transmissionto low cost molded gear sets ideally suited to large quantity productionand marketing.

The main object of the invention is thus to provide a type of powertransmission gearing which will give good service but which can bemanufactured and mounted at a much lower cost than cut gearing.

A further object of the invention is to provide a type of gearing whichcan be operated without lubrication, but which for a given powercapacity is substantially as light in weight and compact as conventionalcut steel gearing.

A further object of the invention is to provide a type of gearing whi hmay be made up entirely of interchangeable formed elements standardizedto a minimum number of sizes.

Other objects of the invention are to produce a type of gearing which isquieter in operation than even precision cut gearing, especially at highspeed; that achieves high efliciency and long Wear-life by virtue of thefact that there is no sliding of the contact surfaces; that may bemanufactured to more liberal tolerances and aligned less precisely thancut steel gears; that will transmit power at a uniform velocity ratio;and will be extremely simple to assemble and mount.

The means to achieve these and other objects and advantages of theinvention will be evident from the drawings as explained in thespecification that follows:

FIG. 1 is a side elevation of a pair of mating spur gears embodying theinvention.

FIG. 2 is an end elevation of the same.

FIG. 3 is a centerline section of the same.

FIG. 4 is an enlarged fragmentary side elevation of a sector of thesmall gear of FIG. 1.

FIG. 5 is a geometric construction showing the manner in which the pitchcircles of mating gears coalesce to form a common intermediate-radiuspitch arc of uniform velocity ratio (zero relative velocity).

FIG. 6 is a side elevation of a pair of mating spur gears showinganother embodiment of the invention.

FIG. 7 is an end elevation of the same.

16. 8 is a centerline section of the same.

PEG. 9 is a View similar to P16. 8 but illustrating two gears securedtogether and showing how wide gears of greater capacity may be built upof the same elements used in narrower gears.

PEG. 10 is an enlarged fragmentary side elevation of a sector of thesmall gear of FIG. 6.

FIG. 11 is a cross section of a bevel the invention.

FIG. 12 is a cross section of an internal gear embodying the invention.

FIG. 13 is a fragmentary section showing a modification of theconstruction of FIG. 12.

FIG. 14 is an enlarged section of a sector of the internal gear of FIG.12.

In detail and referring to FIGS. 1, 2 and, 3, a set of spur gears isshown in which the small gear includes a toothed rim 4i), with aT-shaped section clamped between a pair of dished endplates 41 with aC-shaped section held together with tie bolts 42. The inner portion ofthe end plates 41 is formed into a hub, with slots 4-3 provided for oneor more keys (not shown). Clamps 45 are provided to tighten the innerdiameter of the end plates 4-1 around a shaft (not shown).

In the larger gear, the toothed rim 46 is also clamped between largerend plates 37 by tie bolts 56, but in this case, a separate hub 48 isprovided, with a keyway 49 and setscrew 59. Relative axial movementbetween hub 48 and endplates 47 is prevented by a ridge 51 on the hub 43and relative rotational movement is prevented by widened portions 52 ofridge 5ft projecting into slots 53 in endplates 47. Tie bolts ii. arelocated nonsymmetrically with respect to the center of the gears inorder to insure that one tooth point or space must be directly above thekeyway (4-3, 4*?) which in turn insures that two or more gears mountedin tandem on a shaft with a common keyway will mesh properly with matinggears also having a common keyway.

In FIG. 4 a section through rim iil shows the profile of the teeth 54.The working surfaces are substantially flat and meet almost at a pointat the ends and in a V between adjacent teeth, although the tooth endsand the bottom of the V are sli htly rounded to reduce stressconcentration. In gearing of this type the term pressure angle is usedfor the angle between the flat working surface 36 and a radial linethrough the pitch point (which is the midpoint of the tooth face andalso the point through which the pitch circle 35 passes. This pressureangle 5 should be in the range of 30 to 45, and in most cases in therange 35 to 40. This means that the width of the tooth at its base is atleast 15% greater than the radial height so that each tooth is lesssusceptible of failure by bending than conventional teeth. A sectionthrough the rim 46 of the larger gear would show tooth profiles ofsubstantially the same shape and size (same pressure angle and circularpitch), except possibly in some cases where the material of the rim idis not the same as that of rim The geometric construction of FIG. 5schematically illustrates the principle on which the gearing disclosedin this specification is based. in this drawing the meshing of the teethfill, 31 of a pair of mating gears is shown. One gear has a pitch circlem-m' of radius r and center A. The mating gear has a pitch circle n-n ofradius r and center B. These two gears are mounted so that their centerdistance AB is less than the sum of the radii r and r hence, the twopitch circles interfere in the region pp'. The amount of interferenceshown in FIG. 5 is exaggerated for clarity.

If at least one of the gears is made of a soft pliable material such asrubber, its pitch circle will coalesce with the pitch circle of theother gear and its teeth will conform to those of the other gear alongthe common pitch arc p-p. If the gear centered at B is made of arelatively hard material such as hard plastic or metal, while the gearcentered at A. is made of rubber, the contact are will be p-c-p and willbe substantially on the pitch circle n-n'. Similarly, if the materialsof the two gears are the reverse the contact are will be pap', whichgear embodying will be substantially on the pitch circle m-m'. But ifthe two 'gears are made of materials having substantially the sameelastic properties, the pitch are will lie in :between the arcdp-a-p'and p-c-p", in some intermediate arc pb-p', and the teeth 3t 31 willconformin the manner shown in FIG. 5. r V

The determination of the most desirable proportions for mating gearswill depend on whether or not their elastic properties are thesarne. Forexample, if gear A is rubber and gear B is metal (or other hardmaterial),

, it is not always desirable to employ the same tooth pitch the contactare p-c-p is shorter or longer than the free or unstressed arcdistancep-a-p. This in turn will depend on whether the free radius ofthe rubber roller r is greater or less than r If the two radii areanything but equal, the metal roller will, in elfect, measure out itscircumference on momentarily stretched or compressed rubber, and thevelocity ratio will not be in proportion to the ratio r /r If teeth arenow placed on the two rollers, however, positive engagement between themwill require the velocity ratio to be in proportion to the numberof-teeth on each gear. There are then two possibilities. One is to givethe teeth on the rubber gear a diiferent pitch and pressure angle thanthose on the metal gear. in the case of the particular proportions shownin FIG. 5, the arc p-c-p' is shorter than arc p-a-p (r being greaterthan r hence if the member centered at B were a roller, it would measureout its circumference on material momentarily compressed (in thetangential direction) and thereby cause the mating roller at A to rotatefaster than r /r times the velocity of the roller. at B. If teeth arethen put on these rollers, it may therefore be desirable to put fewerteeth on the rubber roller than r /r times the number of teeth on themetal gear, and hence the circular pitch and pressure angle of theseteeth should be slightly greater than those on the metal gear.

Although dissimilar circular pitches maybe used for custom made gearsets, they are not appropriate for any fully interchangeable system, forthe reason that the appropriate pitch and pressure angle for any rubbergear will depend on whether the diameter of the particular metal gearwith which it is to be mated is larger or smaller than its own diameter.

If on the other hand the pitch and pressure angle are kept the same onboth gears, so that the smaller gear 30 is forced to rotate at r /rtimes the speed of gear 31, then another ditficulty arises; the velocityat the pitch point e is governed by the metal gear and in eifect imposedon the rubber gear. But since the distance ratio Bc/Ac is considerablylarger than the angular velocity ratio r /r the point 0 considered to bein the rubber gear is being urged in the direction of motion much fasterthan it would otherwise go. Hence, a considerable amount of tangentialshear will be set up in the rubber gear, and

the capacity of the rubber gear to carry useful torque of the matinggears.

FIGS. 6, ,7 and 8. rims 15 are retained between two end plates 16 byrespectively proportional to the pitch radius or diameter of the gears.I r I The deformation of each rim in a radial direction bears a directrelationship to the thickness of the rim and an inverse relationship tothe modulus of elasticity of the material of the rim. If a pair ofmating rims are made of rubber of thesame durometer hardness it will beapparent that the deformation under a particular radial loading may bevaried by varying the thickness of the moduli of elasticity it will beapparent that the rim thicknesses may be modified'to take intoconsideration the fact that the material of lower modulus of elasticityundergoes more deformation under the same unit loading than the materialof higher modulus of elasticity."

It may further be demonstrated that a circle constructed to contain thepoints p, p and b as defined above will a have its center at C and'aradius R equal to the reciprocal of the quantity 1/ r minus '1/1' orand'all points on this circle such as D will be removed from gearcentersA- and B by distances AD and BB in exact proportion to the pitchcircle radii r and r The arc pb-p might therefore be thought of as theparticular are of contact for pliable gears of the same pitch that willminimize nonuseful shear in the teeth and rims. It is also the longestarc of contact that may be obtained for a given maximum radial stress ineither Hence, the maximum torque capacity for a pair of gears of givendiameter will generally be obtained by utilizing rims of similar elasticproperties as defined above. Whether or not this optimization of torquecapacity will be a more important consideration than minimizing thefirst cost, since a pair comprising one phenolic or die-cast metal andone rubber gear will be the cheapest combination, will depend on theparticular application.

Referring to FIGS. 6, 7 and 8, the smaller of the two gears shown ismade up of a toothed rim I mounted on a hub 2, with the axial motionbetween these two elements prevented by end plates 3, tied together bymeans of tie bolts 4 extending through holes in the hub 2. A keyway 5and set screw 6 are provided to permit fixing hub 2 to a shaft (notshown).

The larger of the two gears is similar in construction, except that thetoothed rim '7 may, if desired, be of a difierent material than itsmate], the end plates 8 are larger in diameter and a ringshaped spacer 9is interposed between the rim 7 and the hub 19. Tie bolts 11 and keyway12 correspond to tie bolts 4 and key- A way 5 of gear 1.

FIG. 9 shows how a gear of greater torque capacity can be builtup ofelements similar to those shown in In this construction two toothedmeans of longer tie bolts 17, with two ring-shaped spacers 18, 19interposed between each rim l5 and its hub 24 FIG. 10 shows the sawtooth profiles of rim 1 (FIG. 6) and the typical splines 25 that preventrelative rotation between adjacent rims (1, 7, 15), spacers (9, 18, 19)and hubs (2, lit, 26). The pitch circle is 35. The tooth faces 36 shouldbe substantially flat, asin the case of FIG. 4, and should have roundedends and fillets, and should have a pressure angle zp 'of 30 to 45. The

characteristic of the tooth profiles of the mating rim 7 should bear thesame relation to those of rim 1 as in the corresponding parts of FIG. 4,and, hence, if the elastic moduli of both rims are the same, thecircular pitch and pressure angles of both should be the same.

It should be noted that draftsmen sometimes draw gear teethschematically showing fiat sides and sometimes also pointed ends, as ona saw, because the involute curve cannot be drawn with conventionaldrafting equipment (see for example U.S. Pat. No. 2,720,119) Suchschematic showing is clearly not intended to constitute a faithfuldisclosure of the actual gear construc tion.

It will also be noted that splines 25 shown in FIG. are also shown inFIGS. 8 and 9, but only on the lower section of the gears. This isbecause one spline directly above the keyway has been omitted to insurethat the teeth of two or more rims (FIG. 9) mounted in tandem willalign. To achieve this it is necessary that the rims 15 all be eithermarked or manufactured so that ne tooth root or one tooth point bedirectly outward radially from the missing spline tooth.

In FIG. ll showing a bevel gear, a conical toothed rim 1% is held onto aconical hub ill by means of a single endplate 112 and tie bolts 113. Akeyway 11d and setscrew 115 are also provided. Tooth profiles are asshown in 4 or it).

in 12, showing an annular gear, a relatively rigid hub as may beobtained by using a tapered bushing 61 with tightening screws e2,carries an outer shroud 63 with an L-shaped section. Tie bolts 64threaded onto shroud to hold together the hub so, the shroud 63 and thetoothed annulus as.

PEG. 13 shows an alternative to the construction of FIG. 12. in thiscase the shroud 67 has a conical portion d8, so that tightening of tiebolts r59 reduces the pitch diameter of pliable ring as. As is the casewith the external gears of PEG. 1, this type of rim deformation permitshelical teeth to be used instead of straight (if desired) becausetighter will not alter the helix angle. The pressure angle a; (Fl-G. 14)is as defined before: the angle between tooth flank and a radial planethrough the pitch point.

Materials suitable for use in the types of gear rims described aboveshould be reasonably soft or pliable, and should be resilient enough toresist cold flow in the contact zone when the gears are stationary forextended periods. Such materials will be called, for the purposes ofthis specification pliable" because they have a low modu us ofelasticity and resilient because they have a high modulus of resilience(tensile strength squared divided by twice the modulus of elasticity).The fact that such materials are moldable (as well as extrudable)whereas steel is not, is fundamental to their selection for use in thetypes of gearing contemplated her At present the most 5 able materialshaving pliabinty and re ilience are the elastorners.

Pliable resilient teeth of the shapes disclosed herein may beadvantageously used in many gears where the quantity to be manufacturediustifies the preparation of the molds, in which case suitable gearbodies, integral with the rim or otherwise, may be employed which arenot novel. However, the tooth shapes disclosed in the foregoing drawingsand specification lend themselves especially to mass production instandard interchangeable sizes, much as V-belts t -belt pulleys havebeen standardized. Since gear pitch and face Width are not ied togetherby the problems of shaft alignment as in the case of metal to metalgearing, a single standard pitch such as teeth per inch of diameter maybe used, and also a standard face width such as one inch orthree-quarters of inch. Thus all gears will mate with all other gears ofthe system.

Further, if gear bodies are used that interpose spacers and/or endplates of standard sizes between hubs and d rims, the number of partswhich distributors must stock is reduced to approximately the samenumber as in the case of ii-belts. If the standard increments are to bein inches, the sizes available would be as follows:

The various permutations and combinations in which gears constructed asshown in H6. 3 or 8 may be made up out of such standardized elementsreveal that a stock of approximately 260 different parts will allow theassembly of more than 2,080,860 difierent gear sets.

It should be noted that the interference between mating gears, shown asthe distance (1-1) in FIG. 5, must be increased according to the maximumamount of torque to be transmitted, the upper limit of interferencehowever depending chiefly on the allowable radial stress that can beaccommodated by the rim material. in some installations the desiredamount of interference may be obtained by moving the shaft on which ismounted one of the gears closer to the other gear after both gears areassembled onto their respective shafts. In many installations, however,the shafts mounting a pair of mating gears will be journaled into acommon housing and hence will not be movable. In such cases it will bedesirable to increase the pitch diameter of at least one of the gears(or decrease the pitch diameter if it is an internal gear as shown inFlG. 12 or 13) after it is in position. This may readily be accomplishedsimply by tightening of the tie-bolts (4, ll, 17, 42, as, d4, 69, 113)to axially compress the rubber rim. In FIGS. 6, 7, 8 and 9 it ispresumed that the free axial width of the rubber rim (1, 7, 15) isslightly greater than that of both the spacers (9, 19) and the hub (2,-19, 2%). It may also be noted that in FIGS. 3 and 13 the cone angle ofthe dished supporting plates must be increased approximately inproportion to the rim pitch diameter, in order that the interferenceproduced by a given amount of axial tightening will be in proportion torim pitch diameter.

Many of the features disclosed herein may be used separately or combinedin obvious ways other than precisely as shown in the drawings. Forexample, FIGS. 4 and 10 could be considered normal sections of helicalteeth as well as straight teeth. Various combinations of similar ordissimilar plastic, rubber-like or metallic material may be used inmating gear rims. The body construction of FIGS. 1 and 13 is applicableto helical or herringbone teeth, if desired. No set screw is required inhub 2 or ill if the material of the hub is made of any slightly flexiblematerial such as phenolic, which can be made to grip the lrey and shaftby sufficient tightening of the tie bolts. Also, if it is desired toreduce torsional deformation, especially of large gear rims, the rimsmay be reinforced with an interior fabric casing in the same fashion asin automobile tires. It should be noted that the wear characteristics ofthe gears described in this specification may be improved byconventional methods of obtaining high finishes, as by anodizing ofaluminum gears, 01' by chrome or other plating of mold or die surfaces.Also, lubber or neoprene gear rims may be faced with a layer of nylon toimprove tooth wear. The saw toot type of profile could also be alteredto any other intermeshing variety which are able to conform to matingteeth without binding and engage and disengage without interferin Toothfaces need not be completely flat, but may be crowned (i.e., madeslightly convex) if it is desired to reduce somewhat the pressure on theend portion of the teeth; pitch diameter means the diameter of a circlethrough the mid-points of the tooth faces.

In the claims below, the following terms are intended to have thefollowing meanings: formable means adapt ed to being manufactured byforming against a finished die or mold surface with no separatefinishing operation involving scraping, cutting, grinding of materialfrom the tooth surface, as for example, by molding, plastic casting,extruding or die-casting; in section referring to gear teeth means asection taken in a plane perpendicularly, to

formed means that the teeth of one gear, in section, have eflectivelythe same shape as the spaces between teeth in the mating gear. I

I claim:

1. A pair of mating gears having an area of engagement and havingsimilar complementariiy tormed'tooth profiles and respectively mountedfor rotation about spaced apart axes, the spacing between said axesbeing such as to cause compressive deformation of matinggears at thearea of engagement thereof whereby a plurality of teeth of one gear arein mesh with a plurality of teeth of the other gear, the teeth of bothof said gears being formed of resilient pliable material to permit suchcompressive deformation through the teeth of each gear.

2. A pair of mating gears according to claim 1 wherein said gears havedifierent diameters and the deformation of each gear is proportional toits pitch radius.

3. A pair of mating gears according to claim 1 wherein the pitch circlesof said gears coalesce at said area with the common pitch are beingsubstantially the arc of a circle having a radius approximately equal tothe quotient of the product and the difference of the radii of saidpitch circles.

4. A pair of mating gears according to claim 1 wherein said gears areformed with rims of resilient pliable material in which said teeth areformed, and the radial deformation of each of said rims bears a directrelationship to the thickness of the rim and an inverse relationship tothe modulus of elasticity of the material of the rim.

References Cited by the Examiner UNITED STATES PATENTS 315,214 4/85Allen 74-443 584,521 6/97 Rich 74206 680,891 8/01 Smith 742l5 X 820,7895/06 Hutchins 74-443 1,235,734 8/17 Stange 74-443 1,297,835 3/19 Guay74461 2,017,139 10/35 Wood 74--2l6 2,313,445 3/43 Lamb 74461 2,530,76711/50 Hamill 74-46l 2,594,207 4/52 Pierce 74-46l 2,932,992 4/ 60' Larsh74-46-1 DON A. WAITE, Primary Examiner. BROUGHTON G. DURHAM, Examiner.

1. A PAIR OF MATING GEARS HAVING AN AREA OF ENGAGEMENT AND HAVINGSIMILAR COMPLEMENTARILY FORMED TOOTH PROFILES AND RESPECTIVELY MOUNTEDFOR ROTATION ABOUT SPACED APART AXES, THE SPACING BETWEEN SAID AXESBEING SUCH AS TO CAUSE COMPRESSIVE DEFORMATION OF MATING GEARS AT THEAREA OF ENGAGEMENT THEREOF WHEREBY A PLURALITY OF TEETH OF ONE GEAR AREIN MESH WITH A PLURALITY OF TEETH OF THE OTHER GEAR, THE TEETH OF BOTHOF SAID GEARS BEING FORMED OF RESILIENT PLIABLE MATERIAL TO PERMIT SUCHCOMPRESSIVE DEFORMATION THROUGH THE TEETH OF EACH GEAR.